Chapter 23: Q. 3 (page 653)

What are the strength and direction of the electric field at the position indicated by the dot in FIGURE $EX 23.3$ $?$ Specify the direction as an angle above or below horizontal.

Short Answer

Expert verified

The strength of the electric field is $7.63 \times 10^{3} V / m$ .

Step by step solution

Angle of electric field diagram

Figure is,

Calculation for magnitude of E1

The electric field's magnitude is,

$\vec{E} = (E_{2} cosθ - E_{1} cosθ) i - (E_{2} sinθ + E_{1} sinθ) j$

$E_{1}$ :

$E_{1} = \frac{{KQ}_{1}}{{AB}^{2}}$

$E_{1} = \frac{(9 \times 10^{9} N) (3.0 \times 10^{- 9} C)}{(5 \sqrt{2} cm)^{2}}$

$E_{1} = 5.4 \times 10^{3} V / m$

Calculation for magnitude of E2

$E_{2}$ :

$E_{2} = \frac{{KQ}_{2}}{{BC}^{2}}$

$E_{2} = \frac{(9 \times 10^{9} N) (3.0 \times 10^{- 9} C)}{(5 \sqrt{2} cm)^{2}}$

$E_{2} = 5.4 \times 10^{3} V / m$

$ΔABC, sinθ = cosθ = \frac{1}{\sqrt{2}}$

So,

localid="1649136637521" $\vec{E} = (E_{2} cosθ - E_{1} cosθ) i - (E_{2} sinθ + E_{1} sinθ) j$

$\vec{E} = (0) i - (2 \times (5.4 \times 10^{3} V / m) \times \frac{1}{\sqrt{2}}) j$

$\vec{E} = 7.63 \times 10^{3} V / m j$

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What are the strength and direction of the electric field at the position indicated by the dot in FIGURE $EX 23.3$ $?$ Specify the direction as an angle above or below horizontal.

Short Answer

Step by step solution

Angle of electric field diagram

Calculation for magnitude of E1

Calculation for magnitude of E2

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What are the strength and direction of the electric field at the position indicated by the dot in FIGUREEX23.3?Specify the direction as an angle above or below horizontal.

Short Answer

Step by step solution

Angle of electric field diagram

Calculation for magnitude of E1

Calculation for magnitude of E2

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Magnetism

Fluids

Geometrical and Physical Optics

Fundamentals of Physics

Further Mechanics and Thermal Physics

Dynamics

Study anywhere. Anytime. Across all devices.

What are the strength and direction of the electric field at the position indicated by the dot in FIGURE $EX 23.3$ $?$ Specify the direction as an angle above or below horizontal.